with_o the_o material_n of_o powder_n and_o ordnance_n other_o affirm_v that_o a_o monk_n of_o germany_n name_v barthold_n shewart_n otherwise_o call_v the_o black_a upon_o a_o cettatne_n time_n not_o think_v upon_o powder_n or_o ordnance_n in_o the_o year_n of_o our_o lord_n 1300_o have_v in_o his_o mortar_n a_o mixture_n of_o sulphur_n and_o niter_fw-la for_o another_o use_n by_o chance_n a_o coal_n of_o fire_n fall_v into_o the_o same_o cause_v it_o so_o to_o rarify_v and_o blow_v itself_o away_o that_o he_o be_v therewith_o astonish_v search_v into_o the_o cause_n thereof_o &_o upon_o further_a trial_n he_o find_v that_o the_o hot_a and_o dry_a quality_n of_o the_o sulphur_n be_v with_o coal_n and_o moisture_n combine_v and_o wrought_v together_o with_o the_o cold_a and_o moist_a quality_n of_o the_o nyter_n be_v apt_a by_o force_n to_o be_v sudden_o unlose_v with_o great_a rarefaction_n whereby_o by_o little_a and_o little_o he_o bring_v that_o unhappy_a invention_n of_o gunpowder_n and_o gun_n to_o perfection_n to_o make_v use_n thereof_o in_o war_n which_o he_o reveal_v in_o short_a space_n make_v it_o common_a beraldus_n say_v that_o at_o the_o first_o invention_n of_o ordnance_n they_o be_v all_o call_v by_o the_o name_n of_o bombard_n a_o word_n compound_v of_o the_o verb_n bombe_n which_o signify_v to_o sound_n and_o of_o ardco_fw-la to_o burn_v and_o they_o that_o use_v they_o they_o call_v bombardier_n which_o name_n be_v yet_o partly_o retain_v after_o which_o as_o bertholdus_n say_v they_o be_v call_v turacio_n and_o turrafragi_n of_o the_o break_n down_o of_o tower_n and_o wall_n and_o by_o john_n de_fw-fr monte_fw-fr regio_fw-la they_o be_v call_v tormenti_fw-la their_o shot_n sphara_n tormentaria_fw-la and_o the_o gunner_n magistri_fw-la tormentorum_fw-la but_o now_o ordnance_n be_v either_o name_v at_o the_o will_n of_o the_o inventor_n either_o according_a to_o his_o own_o name_n as_o the_o canon_n be_v or_o by_o the_o name_n of_o bird_n and_o beast_n of_o prey_n for_o their_o swiftness_n or_o their_o cruelty_n as_o the_o faulconet_n falcon_n saker_n and_o culver_v etc._n etc._n for_o swiftness_n of_o fly_v as_o the_o basilisk_n serpentine_a aspic_n dragon_n siren_n etc._n etc._n for_o cruelty_n whoseswiftnes_n report_n and_o terriblenes_n be_v proper_o and_o witty_o express_v by_o the_o latin_a poet_n forcastorius_n as_o follow_v continue_v cana_fw-la terrificis_fw-la horentia_fw-la bombis_fw-la aera_fw-la &_o flamifferum_fw-la tormenta_fw-mi imitantia_fw-la fulmen_fw-la corripiunt_fw-la vulcan_n tum_fw-la dumb_a theutonas_n armas_fw-la inventum_fw-la dum_fw-la tela_fw-la jovis_fw-la mortalibus_fw-la afer_n nec_fw-la mora_fw-la signantes_fw-la certam_fw-la sibi_fw-la cuique_fw-la volucrens_fw-la inclusum_fw-la salucrum_fw-la cineres_fw-la sulphurque_fw-la nitrumque_fw-la materiam_fw-la accendunt_fw-la seruatain_n veste_fw-la favilla_fw-la fomite_fw-la correpta_fw-la diffusa_fw-la repent_v furit_fw-la vis_fw-la ignea_fw-la circumsepta_fw-la simulque_fw-la cita_fw-la obice_fw-la rupto_fw-la intrusam_fw-la impellit_fw-la glander_n volat_fw-la illaper_n auras_fw-la stridula_fw-la et_fw-la exanime_n passim_fw-la per_fw-la prata_n iacebunt_fw-la deiectae_fw-la volucres_fw-la magno_fw-la micat_fw-la ignibus_fw-la aer_fw-la cum_fw-la tonitru_fw-la quo_fw-la silua_fw-la omnes_fw-la ripaque_fw-la recurua_fw-la et_fw-la percussa_fw-la imo_fw-la sonuerunt_fw-la aequora_fw-la fundo_fw-la imitate_v by_o the_o author_n in_o english_a thus_o what_o horrid_a roar_v proceed_v from_o bombard_n soul_n by_o air_n make_v fire_n torment_n of_o lightning_n flash_n from_o earth_n exhale_v with_o vapour_n vulcan_n howl_v for_o that_o now_o on_o earth_n man_n can_v make_v thunder_n dash_v ingenious_a art_n now_o ap_v nature_n work_n give_v also_o name_n of_o bird_n and_o beast_n of_o prey_n to_o gun_n wherein_o main_a cruelty_n do_v lurk_v when_o powder_a peter_n coles_n and_o napth_n assay_v to_o force_v the_o spheric_a shot_n t'outflye_v report_n and_o by_o report_n to_o make_v the_o welkin_n roar_v and_o sylvan_a cavern_n echo_v loud_o retort_v batter_v sink_v kill_v yet_o aim_v mischief_n more_o for_o merciless_a they_o will_v spare_v nor_o high_a nor_o low_a poor_a fatherless_a nor_o widow_n will_v they_o know_v the_o devil_n bird_n i_o think_v be_v fit_a name_n to_o call_v they_o by_o that_o spit_v such_o cruel_a flame_n chap._n iii_o where_o ordnance_n be_v first_o use_v in_o these_o part_n paulus_n interianus_n the_o ligurian_a historiographer_n a_o grave_n and_o authentic_a author_n write_v that_o in_o the_o year_n of_o our_o lord_n 1366._o when_o the_o war_n be_v hot_a between_o the_o venetian_n and_o the_o genowese_n certain_a german_n present_v two_o piece_n of_o iron_n ordnance_n wrought_v by_o hand_n unto_o the_o seignory_n of_o venice_n with_o some_o provision_n of_o powder_n and_o leaden_a shot_n who_o receive_v they_o very_o thankful_o especial_o see_v how_o that_o diabolical_a unknown_a fury_n have_v not_o only_o exceed_o fear_v but_o also_o slay_v so_o many_o of_o their_o enemy_n that_o thereby_o they_o prevail_v and_o obtain_v a_o wish_a victory_n against_o their_o adversary_n and_o according_o get_v their_o own_o deseigne_n and_o paulus_n jovius_fw-la in_o his_o three_o book_n report_v that_o the_o first_o field_n ordnance_n that_o be_v use_v in_o italy_n be_v in_o the_o war_n between_o the_o bannitoe_n of_o florence_n and_o the_o house_n of_o medici_n bring_v by_o bartholmeo_n coglioni_n and_o that_o the_o prince_n of_o ferrara_n have_v receive_v a_o hurt_n in_o his_o foot_n by_o a_o shott_n from_o one_o of_o those_o small_a piece_n mount_v upon_o wheel_n as_o he_o note_v the_o prince_n earnest_o complain_v that_o coglioni_n have_v behave_v himself_o that_o day_n very_o malicious_o against_o he_o by_o use_v supernatural_a barbarism_n in_o make_v such_o horrible_a and_o unaccustomed_a tempest_n to_o beat_v and_o spoil_v his_o man_n with_o who_o have_v none_o other_o weapon_n to_o defend_v themselves_o but_o only_a sword_n and_o spear_n laonicus_n chalon_n in_o his_o five_o book_n report_v that_o mahomet_n the_o great_a turk_n at_o the_o siege_n of_o constantinople_n in_o the_o year_n of_o our_o lord_n 1419_o plant_v against_o it_o one_o piece_n of_o ordnance_n that_o he_o discharge_v seven_o time_n in_o one_o day_n which_o convey_v a_o bullet_n of_o 300_o pound_n weight_n and_o make_v the_o ground_n tremble_v a_o furlong_n round_o about_o it_o at_o the_o discharge_n with_o the_o report_n thereof_o and_o he_o further_o affirm_v that_o the_o grecian_n answer_v he_o again_o with_o piece_n that_o shoot_v bullet_n of_o 150_o pound_n weight_n pollider_n virgil_n in_o his_o five_o book_n of_o the_o english_a history_n write_v that_o in_o the_o year_n of_o our_o lord_n 1425_o in_o the_o begin_n of_o the_o reign_n of_o the_o french_a king_n charles_n the_o seven_o the_o english_a have_v besiege_v the_o town_n of_o mantz_n so_o batter_v the_o wall_n thereof_o that_o they_o soon_o fall_v to_o the_o ground_n and_o munster_n in_o his_o second_o volume_n write_v that_o the_o duke_n de_fw-fr bar_n 1431_o be_v defeat_v by_o the_o count_n de_fw-fr vademont_n by_o mean_n of_o the_o ordnance_n that_o he_o use_v both_o canon_n and_o culver_v which_o be_v a_o matter_n then_o so_o new_a and_o rare_a that_o the_o count_n himself_o at_o the_o shoot_v they_o off_o fall_v always_o on_o his_o face_n to_o the_o ground_n for_o fear_n ordnance_z be_v also_o use_v by_o the_o almain_n about_o the_o coast_n of_o denmark_n in_o the_o year_n 1434._o paulus_n jovius_fw-la and_o guichardine_n relate_v that_o charles_n the_o eight_o of_o france_n have_v undertake_v the_o conquest_n of_o naples_n use_v ordnance_n both_o in_o the_o plane_n and_o upon_o the_o top_n of_o high_a mountain_n and_o the_o italian_n that_o descrb_v his_o return_n say_v that_o with_o his_o soldier_n he_o draw_v they_o up_o over_o the_o top_n of_o the_o appenyne_n mountain_n and_o so_o from_o place_n to_o place_n with_o admirable_a courage_n where_o by_o reason_n of_o the_o steepnesse_n and_o roughness_n of_o the_o place_n horse_n and_o cattle_n can_v not_o be_v employ_v to_o draw_v they_o but_o his_o horseman_n do_v then_o carry_v the_o shot_n &_o other_o munition_n to_o they_o pierrier_n steinhuchsen_n cap._n 3._o abatte_fw-mi mur._n maurbrecher_n cap._n 4._o pierrier_n ou_fw-fr bombarde_n steinbuchse_n eschelle_n a_o mire_n qiel_n leittern_n cap._n 5._o tract_n 2._o cap._n 6._o tract_n the_o l'espaulle_a avec_fw-fr ses_fw-fr tronier_n et_fw-fr explanade_n figur_n der_fw-mi schutren_n mitt_fw-ge ihren_n zangen_fw-mi und_fw-ge britschen_fw-ge belong_v each_o of_o they_o alittle_o camello_n vitelli_n be_v say_v to_o have_v invent_v the_o pistol_n and_o small_a hand-gunues_a for_o horseman_n whereby_o ferdinand_n of_o arragon_n discomfit_v the_o french_a and_o almain_n musket_n be_v invent_v for_o footman_n and_o first_o use_v at_o the_o siege_n of_o rhege_n in_o 1521_o since_o which_o time_n their_o invention_n have_v be_v so_o infinite_o vary_v as_o no_o man_n can_v full_o express_v which_o now_o shall_v suffice_v i_o and_o i_o hope_v
demand_v 3_o that_o the_o piece_n give_v to_o be_v prepare_v have_v she_o ordinary_a carriage_n and_o platform_n give_v so_o right_a and_o due_o fit_v as_o will_v neither_o cause_n nor_o suffer_v the_o piece_n deliver_v and_o reverse_v to_o start_v from_o the_o level_a or_o direction_n give_v demand_v 4._o that_o the_o shot_n keep_v his_o course_n so_o from_o his_o due_a rest_a place_n in_o the_o cavity_n of_o the_o piece_n unto_o the_o point_v blank_a or_o end_n of_o the_o right_n range_v thereof_o so_o as_o that_o the_o centre_n of_o it_o be_v always_o in_o the_o axis_n of_o the_o boar_n suppose_v infinite_o to_o proceed_v without_o any_o sensible_a declination_n from_o the_o same_o the_o faid_n bear_v be_v part_n of_o the_o way_n of_o the_o say_v shoot_v and_o the_o direct_a of_o theresidue_n of_o the_o course_n of_o the_o same_o demand_v 5._o that_o the_o point_v blank_a or_o right_a line_n or_o range_v be_v that_o point_n in_o the_o axis_n of_o the_o boar_n imagine_v to_o proceed_v and_o be_v infinite_o continue_v unto_o that_o place_n where_o the_o centre_n of_o the_o shot_n shall_v in_o his_o course_n sensible_o begin_v to_o decline_v from_o the_o say_v continue_v imagine_v axis_n downward_o demand_v 6._o that_o the_o visible_a right_a line_n make_v or_o imagine_v to_o pass_v from_o the_o breech_n of_o the_o piece_n to_o the_o mouth_n of_o the_o same_o upon_o the_o high_a ring_n or_o supersicies_n of_o the_o mettle_n she_o lie_v on_o her_o catiage_n and_o platform_n be_v call_v the_o middle_a line_n of_o the_o piece_n demand_v 7._o that_o the_o visible_a right_a line_n make_v or_o imagine_v to_o pass_v from_o the_o breech_n to_o the_o mouth_n upon_o the_o surface_n of_o the_o mettle_n vertical_o over_o the_o axis_n of_o the_o boar_n of_o the_o same_o piece_n she_o lie_v upon_o her_o carriage_n and_o platform_n give_v be_v call_v the_o large_a line_n of_o that_o piece_n demand_v 8._o that_o the_o short_a distance_n between_o the_o vertical_a plane_n of_o the_o axis_n of_o the_o body_n of_o the_o piece_n and_o the_o vertical_a plane_n of_o the_o axis_n of_o the_o soul_n or_o boar_n of_o the_o same_o piece_n take_v upon_o the_o baseringe_v at_o the_o breech_n thereof_o for_o the_o carriage_n piece_n and_o platform_n give_v be_v call_v the_o large_a of_o that_o piece_n maxim_n of_o natural_a philosophy_n necessary_a to_o be_v first_o know_v 1_o every_o motion_n in_o the_o world_n end_v in_o repose_n 2_o all_o motion_n be_v make_v upon_o some_o quantity_n 3._o every_o simple_a body_n be_v either_o rare_a and_o light_a or_o else_o thick_a and_o heavy_a and_o according_a to_o these_o difference_n it_o be_v natural_o carry_v towards_o some_o part_n 4_o the_o world_n have_v high_a or_o upward_o and_o low_a or_o downward_o and_o the_o low_a depend_v upon_o the_o influence_n of_o the_o high_a 5_o the_o rare_a body_n mount_v the_o fire_n more_o than_o the_o air_n the_o thick_a and_o gross_a body_n descend_v the_o earth_n more_o than_o the_o water_n 6_o the_o light_a be_v more_o movable_a than_o the_o heavy_a 7_o nothing_o work_v natural_o in_o that_o which_o be_v whole_o like_a or_o whole_o dislike_v but_o in_o that_o which_o be_v contrary_a to_o it_o and_o more_o feeble_a 8_o the_o form_n work_v be_v aid_v by_o the_o quality_n as_o the_o matter_n suffer_v which_o suffer_v by_o the_o quantity_n 9_o nature_n be_v extreme_o curious_a as_o well_o of_o her_o perfection_n as_o of_o her_o conservation_n and_o then_o when_o all_o thing_n conspire_v 10_o aswell_o the_o action_n that_o come_v from_o the_o agent_n as_o the_o passion_n from_o the_o patienthath_n proportion_n 11_o accident_n take_v his_o unity_n from_o the_o subject_n and_o go_v not_o from_o one_o thing_n to_o another_o theorem_fw-la 1._o every_o corporal_a thing_n repose_v in_o its_o natural_a place_n light_n body_n 〈◊〉_d towards_o the_o heaven_n upward_o and_o heavy_a body_n towards_o the_o earth_n centre_n downward_o each_o body_n be_v light_a or_o heavy_a if_o it_o be_v heavy_a it_o will_v then_o move_v downward_o if_o light_n upward_o now_o the_o circular_a motion_n be_v neither_o upward_o or_o downward_o therefore_o no_o motion_n can_v be_v circular_a but_o by_o violence_n theor._n 2._o motion_n may_v be_v make_v in_o any_o place_n within_o the_o moon_n orb_n every_o thing_n that_o be_v within_o the_o lunar_a orb_n may_v make_v motion_n or_o change_n theor._n 3_o before_o any_o thing_n move_v towards_o its_o natural_a place_n from_o its_o first_o be_v it_o go_v stretch_v unto_o the_o natural_a measure_n neither_o augmentation_n nor_o diminution_n be_v make_v but_o only_o by_o change_v of_o the_o quality_n or_o form_n for_o the_o quality_n alone_a incontinent_o follow_v new_a generation_n do_v cause_n either_o stretch_v or_o shrink_v and_o true_a it_o be_v that_o in_o such_o mooving_n as_o tend_v unto_o the_o entire_a ruin_n of_o the_o form_n the_o just_a dimension_n be_v not_o find_v to_o be_v but_o either_o great_a or_o lesser_a according_a to_o the_o quantity_n agitate_v most_o forcible_o therein_o and_o so_o it_o move_v most_o violent_a and_o long_a theor._n 4._o nature_n admit_v no_o emptynesse_n nature_n pursue_v and_o entertain_v perfection_n as_o much_o as_o be_v possible_a now_o the_o perfection_n of_o motion_n be_v the_o end_n thereof_o namely_o the_o repose_n that_o the_o simple_a body_n will_v find_v either_o upward_o or_o downward_o in_o all_o place_n therefore_o in_o the_o elementary_a universe_n they_o affect_v their_o repose_n either_o upward_o or_o downward_o so_o there_o be_v not_o by_o nature_n any_o such_o thing_n as_o vacuity_n for_o the_o avoid_v of_o which_o nature_n make_v heavy_a thing_n mount_v and_o light_a thing_n descend_v whereby_o marvelous_a thing_n be_v perform_v as_o we_o may_v see_v by_o our_o pump_n which_o make_v water_n ascend_v as_o high_a as_o the_o cloud_n and_o by_o the_o spirituall_n the_o air_n be_v retain_v beneath_o and_o diverse_a other_o effect_n seem_v so_o miraculous_a to_o such_o as_o see_v they_o as_o they_o cause_v they_o to_o wonder_v thereat_o for_o whence_o come_v it_o that_o a_o vessel_n of_o marble_n fill_v with_o water_n when_o the_o water_n come_v to_o be_v freeze_v into_o you_o that_o it_o break_v the_o same_o though_o a_o foot_n thick_a but_o that_o the_o water_n thickn_v thereby_o and_o so_o break_v the_o volume_n of_o the_o ordinary_a quantity_n thereof_o the_o cause_n precead_v the_o effect_n follow_v so_o also_o a_o narrow_a neck_a bottle_n fill_v with_o liquor_n and_o turn_v the_o bottom_n upward_o yet_o retain_v the_o liquor_n from_o run_v out_o because_o air_n can_v enter_v therein_o to_o fill_v the_o place_n whereupon_o we_o may_v judge_v that_o the_o law_n of_o fullness_n be_v more_o general_a and_o precede_v that_o of_o the_o move_a of_o simple_a body_n theor._n 5._o every_o body_n have_v a_o place_n a_o point_n which_o can_v be_v mark_v in_o essence_n not_o have_v any_o part_n be_v no_o body_n and_o therefore_o be_v contrary_a to_o the_o hypothesis_n but_o a_o body_n have_v place_n of_o dimension_n so_o if_o the_o surface_n of_o the_o body_n which_o approach_v on_o all_o side_n and_o touch_v every_o where_o tie_v the_o superficies_n to_o close_v the_o body_n it_o be_v then_o in_o such_o a_o place_n as_o have_v the_o very_a same_o dimension_n within_o that_o the_o body_n have_v without_o or_o else_o there_o must_v be_v emptiness_n which_o by_o the_o precedent_n be_v absurd_a theor._n 6._o a_o body_n rarify_n its_o self_n the_o place_n thereof_o increase_v as_o the_o body_n increase_v as_o a_o body_n of_o earth_n that_o then_o contain_v one_o solid_a foot_n in_o measure_n be_v make_v water_n which_o add_v thereto_o one_o other_o solid_a foot_n the_o place_n also_o must_v increase_v from_o one_o to_o two_o solid_a foot_n or_o else_o it_o have_v not_o the_o same_o just_a dimension_n within_o that_o the_o body_n have_v without_o and_o so_o it_o be_v not_o the_o place_n of_o that_o body_n of_o water_n so_o if_o the_o place_n also_o be_v great_a than_o the_o body_n fill_v there_o must_v in_o that_o place_n be_v emptiness_n between_o it_o and_o the_o body_n which_o be_v absurd_a therefore_o the_o place_n increase_v as_o the_o body_n ratify_v do_v theor._n 7._o two_o body_n can_v be_v together_o in_o one_o and_o the_o same_o place_n if_o several_a body_n can_v be_v together_o all_o the_o member_n of_o one_o same_o body_n may_v also_o have_v one_o and_o the_o same_o place_n and_o each_o part_n may_v one_o fall_v into_o the_o range_n of_o the_o other_o which_o be_v to_o take_v away_o from_o the_o quantity_n the_o true_a nature_n thereof_o and_o which_o by_o its_o essential_a property_n set_v out_o the_o part_n several_o one_o from_o another_o nevertheless_o that_o some_o sleight_n appearance_n have_v seem_v to_o yield_v
the_o gunner_n show_v the_o whole_a practice_n of_o artillery_n with_o all_o the_o appurtenance_n thereunto_o belong_v together_o with_o the_o make_n of_o extraordinary_a artificial_a firework_n as_o well_o for_o pleasure_n and_o triumph_n as_o for_o war_n and_o service_n write_v by_o robert_n norton_n one_o of_o his_o majesty_n gunner_n and_o enginier_n london_n print_v by_o a._n m._n for_o humphrey_n robinson_n and_o be_v to_o be_v sell_v at_o the_o three_o pigeon_n in_o paules-churchyard_n 1628._o to_o the_o imperial_a majesty_n of_o great_a britain_n france_n and_o ireland_n king_n charles_n almighty_a god_n have_v make_v your_o majesty_n sovereign_a over_o many_o strong_a nation_n natural_o martial_a and_o artificial_o exercise_v in_o arm_n yet_o if_o they_o want_v discipline_n though_o many_o they_o be_v but_o few_o and_o though_o else_o strong_a yet_o therefore_o weak_a your_o mighty_a kingdom_n also_o be_v strong_o situate_v by_o nature_n entrench_v about_o with_o a_o broad_a dike_n the_o sea_n pallisadoe_v with_o rock_n and_o sand_n sentinel_v with_o strange_a set_v tide_n of_o ebb_n and_o flood_n defend_v by_o frequent_a storm_n and_o tempest_n high_o inritch_v with_o fertillity_n of_o nature_n furnish_v plenteous_o with_o all_o manner_n of_o material_o fit_v the_o felicity_n of_o man_n life_n upon_o earth_n both_o for_o time_n of_o peace_n and_o war_n so_o that_o nothing_o can_v seem_v to_o be_v more_o wish_v for_o if_o industry_n be_v use_v but_o especial_o if_o correspondency_n be_v find_v in_o a_o good_a and_o due_a temper_n between_o the_o head_n and_o the_o member_n as_o perfect_a obedience_n and_o service_n from_o the_o member_n to_o the_o head_n and_o entire_a love_n and_o care_n from_o the_o head_n to_o the_o member_n for_o their_o good_a and_o safety_n gun_n your_o majesty_n have_v but_o want_v gunner_n because_o they_o want_v respect_n and_o encouragement_n let_v occasion_n be_v rule_v with_o reason_n war_n manage_v with_o discipline_n judgement_n and_o policy_n let_v stubborn_a offender_n be_v punish_v deserve_v man_n prefer_v eminent_a place_n not_o grant_v for_o favour_n to_o insufficient_a man_n or_o stranger_n have_v honest_a subject_n far_o more_o able_a to_o perform_v the_o service_n so_o we_o shall_v all_o make_v holiday_n to_o serve_v our_o god_n obey_v our_o king_n and_o enjoy_v god_n blessing_n bestow_v upon_o we_o every_o man_n eat_v his_o grape_n under_o his_o own_o vine_n without_o fear_n of_o foreign_a enemy_n to_o conclude_v then_o nothing_o can_v be_v want_v man_n money_n mean_n nor_o prosperity_n when_o the_o god_n of_o order_n have_v settle_v such_o a_o congruity_n now_o that_o your_o majesty_n may_v the_o better_o be_v provide_v hereafter_o of_o understand_v gunner_n to_o manage_v your_o artillery_n the_o powerful_a regent_n of_o modern_a war_n i_o have_v endeavour_v in_o this_o practice_n of_o artillery_n to_o supply_v their_o want_n the_o best_a i_o can_v not_o doubt_v but_o in_o short_a time_n it_o may_v work_v good_a effect_n therein_o if_o your_o majesty_n will_v be_v gracious_o please_v to_o countenance_v these_o few_o line_n under_o your_o royal_a patronage_n my_o wrong_n and_o discouragement_n have_v hitherto_o hinder_v the_o publication_n hereof_o which_o if_o your_o majesty_n will_v be_v please_v to_o refer_v to_o be_v examine_v and_o relieve_v according_o it_o will_v then_o appear_v i_o have_v cause_n to_o speak_v and_o i_o shall_v be_v again_o encourage_v for_o great_a and_o further_a service_n hereafter_o so_o most_o humble_o crave_v pardon_n for_o my_o boldness_n prostrate_v myself_o at_o your_o sacred_a foot_n as_o by_o oath_n and_o duty_n bind_v will_v ever_o remain_v your_o most_o faithful_a and_o loyal_a subject_n and_o servant_n robert_n norton_n to_o mr._n robert_n norton_n and_o his_o practice_n of_o artillery_n when_o first_o i_o know_v the_o difference_n of_o time_n and_o several_a climate_n of_o the_o world_n round_a globe_n i_o then_o think_v artist_n fit_a man_n to_o climb_v to_o honour_n and_o to_o wear_v the_o golden_a robe_n but_o now_o these_o time_n do_v differ_v from_o that_o time_n stranger_n respect_v be_v by_o courtier_n crime_n then_o when_o i_o know_v the_o sea_n my_o whole_a delight_n be_v how_o to_o trim_a a_o ship_n prepare_v for_o war_n but_o all_o be_v vain_a till_o gunner_n skill_n and_o may_v with_o practise_a force_n all_o excel_v so_o far_o let_v seaman_n land-man_n all_o man_n true_o know_v that_o gunner_n art_n be_v of_o substance_n not_o of_o show_n the_o land-man_n he_o most_o bold_o make_v approach_n with_o horse_n and_o foot_n with_o sword_n and_o shield_n and_o spear_n but_o all_o be_v vain_a he_o never_o can_v encroach_v if_o gun_n and_o gunner_n shall_v be_v want_v there_o therefore_o such_o artist_n sure_o it_o be_v best_o to_o cherish_v and_o expert_a gunnered_a engeneer_n to_o nourish_v for_o proof_n whereof_o let_v every_o artist_n view_n why_o such_o man_n shall_v not_o to_o preferment_n mount_v peruse_v this_o book_n its_o lynes_n and_o fgure_n true_a so_o may_v he_o find_v the_o difference_n of_o account_n betwixt_o the_o english_a and_o the_o dutch_a norton_n and_o bear_v then_o give_v our_o own_o their_o due_a without_o demor_fw-la lege_fw-la moratur_fw-la in_o lege_fw-la but_o norton_n i_o have_v be_v something_o to_o bold_a to_o paraphrase_n upon_o thy_o worth_n and_o quality_n because_o i_o want_v sufficient_a to_o unfold_v they_o and_o th'ingenious_a work_n reality_n let_v this_o suffice_v thy_o praise_n will_v show_v itself_o it_o be_v worth_a the_o golden-fleece_n the_o indian_a pelf_n captain_n john_n butler_n a_o due_a to_o the_o author_n his_o work_n and_o worth_n since_o among_o all_o nation_n war_n itself_o do_v show_v it_o behoove_v man_n war_n weapon_n for_o to_o know_v who_o here_o may_v learn_v the_o gunner_n aim_v art_n which_o thy_o free_a industry_n to_o all_o impart_v the_o fit_a subject_n now_o it_o be_v by_o far_o at_o these_o time_n when_o such_o rumour_n be_v of_o war_n and_o fill_v the_o ear_n and_o courage_n awake_v go_v on_o then_o and_o to_o thou_o this_o glory_n take_v that_o he_o that_o read_v these_o thing_n which_o thou_o do_v write_v may_v know_v a_o gunner_n part_n though_o he_o never_o fight_v and_o know_v war_n chief_a engine_n use_v and_o strength_n in_o boar_n cilind_a axis_n and_o in_o length_n in_o touchhole_n carriage_n wadd_a in_o shot_n and_o charge_n of_o firework_n in_o brief_a thou_o speak_v at_o large_a french_a spanish_a dutch_a italian_a vail_v your_o cap_n to_o nortons_n skill_n in_o mars_n his_o thunderclaps_a john_n rudstone_n a_o lover_n of_o the_o art_n mathematical_a theoric_n and_o practic_n to_o his_o good_a friend_n master_n robert_n norton_n on_o his_o practice_n of_o artillery_n i_o tell_v you_o friend_n before_o your_o book_n i_o will_v write_v but_o not_o idolatrise_v with_o poetic_a spirit_n do_v our_o love_n much_o wrong_n in_o little_a right_n the_o time_n necessity_n and_o each_o studious_a mind_n will_v make_v it_o praise_v itself_o which_o you_o shall_v find_v by't_n oft_o impression_n thou_o be_v being_n here_o refine_v yet_o just_o i_o confess_v i_o have_v be_v show_v book_n that_o sell_v well_o yet_o not_o for_o what_o be_v their_o own_o but_o for_o commendator_n before_o they_o know_v and_o this_o integrity_n command_v i_o say_v that_o to_o the_o truth_n thou_o show_v the_o right_a way_n for_o young_a artist_n and_o here_o the_o old_a may_v stay_v for_o here_o they_o be_v satissy_v with_o small_a dispense_n of_o purse_n or_o brain_n of_o skill_n the_o quintessence_n draw_v from_o the_o antic_a artist_n excellence_n i_o know_v rich_a jewel_n may_v themselves_o commend_v which_o be_v such_o book_n that_o for_o the_o public_a end_n with_o judgement_n write_v be_v so_o thy_o good_a friend_n richard_n robinson_n in_o the_o due_a honour_n of_o the_o author_n master_n robert_n norton_n and_o his_o worke._n perfection_n if_o it_o have_v ever_o be_v attain_a in_o gunner_n art_n this_o author_n have_v it_o gain_v by_o study_n and_o experience_n and_o he_o the_o fruit_n of_o all_o his_o pain_n have_v offer_v thou_o a_o present_a well_o befit_v this_o our_o age_n when_o all_o the_o world_n be_v but_o a_o martial_a stage_n let_v sweet_a study_n lull_v a_o sleep_n and_o please_v man_n who_o presume_v security_n but_o these_o thy_o labour_n practise_v shall_v more_o safe_o guard_v those_o that_o foresee_v the_o danger_n the_o other_a bare_a this_o benefit_n we_o soldier_n do_v embrace_v this_o rare_a and_o useful_a work_n and_o over_o the_o face_n of_o all_o the_o world_n let_v thy_o fame_n echo_n sound_n more_o than_o that_o roar_a engine_n and_o redound_v to_o the_o honour_n of_o our_o nation_n that_o thy_o pain_n transcend_v all_o former_a and_o their_o glory_n stain_v captain_n john_n smith_n hungariensis_n a_o table_n of_o the_o content_n definition_n page_n 1_o demand_n page_n 2_o
swister_n and_o strong_a be_v the_o stroke_n now_o to_o move_v more_o be_v to_o act_v more_o in_o corporal_a thing_n and_o the_o more_o quick_a the_o action_n be_v so_o much_o the_o strong_a wherefore_o according_a to_o the_o measure_n of_o the_o agent_n motion_n the_o swiftness_n of_o the_o course_n the_o stroke_n be_v reckon_v strong_a this_o be_v the_o enginieres_n helicon_n from_o whence_o the_o most_o of_o their_o strong_a engine_n be_v draw_v the_o greatness_n of_o the_o distance_n be_v nothing_o if_o the_o time_n be_v long_o nor_o the_o shortness_n of_o the_o time_n if_o the_o distance_n be_v short_a theor._n 13._o there_o can_v be_v no_o move_n in_o action_n make_v more_o violent_a then_o with_o a_o piece_n of_o ordnance_n the_o volume_n or_o extent_n of_o the_o rarefaction_n be_v ten_o time_n as_o much_o when_o it_o become_v fire_n as_o it_o be_v when_o it_o be_v earth_n fire_n be_v ten_o time_n more_o rare_a than_o earth_n theor_n by_o the_o 5._o max._n by_o the_o 4._o theor_n and_o of_o all_o nature_n agent_n the_o fire_n and_o of_o all_o the_o quality_n beat_v carry_v away_o the_o prize_n for_o violence_n see_v the_o generation_n of_o fire_n in_o the_o powder_n be_v momentary_a therefore_o the_o time_n of_o the_o rarefaction_n be_v extreme_o short_a as_o be_v of_o one_o only_a instant_n if_o any_o moment_n before_o that_o generation_n begin_v not_o to_o drive_v out_o the_o bullet_n the_o stroke_n must_v then_o be_v extreme_o violent_a see_v that_o the_o distance_n be_v very_o great_a in_o respect_n of_o the_o shortness_n of_o the_o time_n meteor_n ariss_n 2._o meteor_n unto_o which_o we_o may_v add_v the_o quickness_n of_o the_o flame_n which_o be_v such_o that_o it_o will_v not_o stay_v here_o below_o the_o least_o part_n of_o time_n but_o will_v fly_v away_o theor._n 14._o the_o long_a the_o chase_n of_o the_o piece_n the_o strong_a the_o streak_n the_o generation_n of_o this_o fire_n be_v make_v in_o a_o instant_n the_o rarity_n arive_v at_o once_o the_o violence_n press_v to_o chase_v out_o the_o shot_n the_o flame_n fly_v make_v it_o issue_v out_o theorem_a by_o the_o ten_o theorem_a and_o air_n to_o come_v in_o to_o prevent_v emptiness_n and_o all_o as_o it_o be_v in_o a_o instant_n therefore_o the_o long_a the_o chase_n of_o the_o piece_n be_v be_v fortify_v and_o load_v according_o the_o more_o effectual_a shall_v the_o action_n be_v and_o the_o stroke_n the_o more_o violent_a whereby_o it_o come_v to_o pass_v that_o long_a culvering_n carry_v further_o then_o great_a canon_n although_o with_o less_o powder_n yet_o the_o force_n be_v better_a entertain_v by_o their_o great_a length_n and_o better_a fortification_n to_o endure_v the_o full_a charge_n of_o powder_n theor._n 15._o a_o piece_n reverse_v when_o it_o discharge_v when_o the_o ignition_n begin_v at_o the_o bottom_n of_o the_o concave_n of_o the_o piece_n at_o the_o touch_n hole_n the_o piece_n reverse_v at_o the_o instant_n of_o the_o rarefaction_n the_o vent_n it_o can_v find_v be_v only_o forth_o of_o the_o touchhole_n beat_v back_o until_o the_o shot_n be_v go_v out_o and_o this_o make_v a_o piece_n mount_v to_o shoot_v from_o alow_o upward_o to_o reverse_v more_o then_o upon_o the_o level_a or_o from_o aloft_o downward_o for_o that_o the_o shot_n which_o be_v heavy_a and_o consequent_o violent_a in_o his_o natural_a descend_v when_o it_o be_v force_v upward_o it_o resist_v more_o than_o either_o shot_n downward_o or_o level_n and_o so_o the_o more_o the_o weight_n of_o the_o bullet_n resist_v the_o force_n that_o drive_v out_o the_o shot_n which_o at_o last_o it_o be_v constrain_v to_o obey_v and_o to_o yield_v the_o more_o to_o the_o reverse_a but_o the_o metal_n suffer_v the_o more_o when_o it_o be_v resist_v as_o some_o man_n cause_v it_o by_o make_v a_o rampart_n behind_o the_o breech_n of_o the_o piece_n against_o which_o it_o may_v stay_v thereby_o to_o augment_v the_o force_n of_o the_o shot_n from_o whence_o we_o may_v gather_v that_o the_o impression_n of_o reverse_n be_v only_o whileft_v the_o shot_n be_v within_o the_o piece_n beside_o the_o touchhole_n be_v make_v near_o the_o bottom_n of_o the_o concave_n do_v not_o only_o augment_v the_o reverse_v more_o than_o if_o the_o touchhole_n be_v in_o the_o midst_n of_o the_o powder_n or_o rather_o more_o forward_o whereby_o the_o powder_n will_v fire_v together_o in_o the_o less_o time_n and_o little_a or_o none_o go_v out_o unfired_a reverse_a less_o and_o make_v the_o fury_n of_o the_o shoot_v the_o great_a and_o this_o make_v the_o small_a pistol_n so_o pierce_v to_o out_o shoot_v those_o that_o have_v their_o touch-hole_n pierce_v at_o the_o bottom_n of_o their_o bore_n theor._n 16._o a_o piece_n of_o ordnance_n sheot_v further_a in_o a_o right_a line_n from_o a_o low_a upward_o then_o from_o above_o downward_o except_o perpendicular_o to_o the_o shot_n make_v upward_o there_o be_v great_a resistance_n of_o the_o bullet_n but_o when_o a_o shot_n be_v make_v downward_o the_o force_n do_v not_o only_o work_v but_o the_o weight_n of_o the_o shot_n also_o by_o its_o natural_a heaviness_n the_o bullet_n easy_o descend_v from_o the_o strait_a line_n fall_v under_o expectation_n whence_o it_o come_v that_o the_o right_n range_v be_v further_a in_o mounture_n then_o in_o any_o imbasure_n for_o this_o proposition_n be_v not_o to_o be_v understand_v so_o at_o the_o go_v out_o of_o the_o shot_n for_o all_o right_n range_v be_v all_o equal_o strait_a nevertheless_o that_o it_o be_v short_a shoot_v from_o aloft_o downward_o and_o long_a upward_o and_o the_o level_a be_v the_o mean_a between_o they_o both_o theor._n 17._o there_o be_v three_o chief_n most_o material_a and_o efficient_a cause_n of_o the_o great_a violence_n of_o any_o shot_n make_v out_o of_o great_a ordnance_n viz._n the_o powder_n the_o piece_n and_o the_o weight_n of_o the_o bullet_n theor._n 18._o powder_n be_v compound_v of_o three_o principle_n or_o element_n saltpetre_n sulphur_n and_o cole_n whereof_o saltpetre_n be_v it_o that_o give_v the_o chief_a violence_n theor._n 19_o albeit_o saltpetre_n be_v indeed_o the_o only_a or_o most_o material_a cause_n of_o the_o violence_n and_o that_o powder_n common_o find_v most_o forcible_a that_o be_v rich_a of_o petre_n yet_o be_v there_o a_o certain_a proportion_n of_o perfection_n of_o these_o three_o component_n and_o that_o in_o such_o sort_n as_o if_o you_o add_v more_o or_o less_o petre_n the_o violence_n shall_v abate_v theor._n 20._o although_o powder_n be_v also_o the_o most_o efficient_a cause_n of_o the_o force_n and_o violence_n of_o any_o shot_n yet_o be_v there_o such_o a_o proportional_a charge_n of_o powder_n to_o be_v find_v for_o every_o several_a piece_n in_o regard_n of_o the_o proportion_n of_o she_o charge_v and_o vacant_a cylinder_n as_o give_v more_o or_o less_o than_o the_o same_o proportional_a charge_n it_o shall_v diminish_v and_o not_o increase_v the_o violence_n of_o the_o shot_n theor._n 21._o if_o any_o two_o bullet_n of_o equal_a quantity_n but_o unequal_a weight_n be_v let_v fall_v from_o any_o lofty_a place_n to_o the_o horizon_n the_o more_o weighty_a shall_v ever_o fall_v the_o more_o swift_o albeit_o not_o porportional_o to_o their_o weight_n which_o axiom_n be_v indeed_o erroneous_a albeit_o a_o great_a philosopher_n have_v aver_v the_o same_o theor._n 22._o if_o two_o equal_a bullet_n of_o different_a weight_n be_v shoot_v out_o of_o one_o and_o the_o same_o piece_n direct_o to_o the_o zenith_n both_o bullet_n be_v of_o massy_a mettle_n and_o charge_v with_o one_o quantity_n and_o kind_n of_o powder_n the_o light_a shall_v always_o outflie_o the_o heavy_a but_o such_o kind_n of_o bullet_n they_o may_v be_v charge_v with_o all_o as_o the_o heavy_a shall_v outflie_o the_o light_a although_o they_o be_v both_o discharge_v with_o the_o same_o piece_n and_o quantity_n of_o the_o same_o powder_n theor._n 23._o there_o be_v such_o a_o convenient_a weight_n to_o be_v find_v of_o the_o bullet_n in_o respect_n of_o the_o powder_n and_o piece_n as_o the_o bullet_n mettle_n be_v either_o heavy_a or_o light_a than_o that_o weight_n shall_v rather_o hinder_v then_o further_o the_o violence_n or_o far_o range_v of_o the_o shot_n theor._n 24._o there_o be_v such_o a_o convenient_a proportion_n to_o be_v find_v of_o the_o length_n of_o every_o piece_n to_o his_o boar_n or_o bullet_n diametre_fw-la in_o respect_n of_o the_o powder_n and_o weight_n of_o the_o ball_n as_o either_o increase_n or_o diminish_v that_o proportion_n it_o shall_v abate_v also_o and_o hinder_v the_o violence_n of_o the_o shot_n theor._n 25._o this_o proportion_n exact_o find_v in_o any_o one_o piece_n do_v not_o hold_v in_o all_o other_o and_o yet_o the_o difference_n and_o alteration_n be_v such_o as_o may_v be_v
reduce_v to_o rule_n certain_a theor._n 26._o beside_o these_o three_o most_o material_a cause_n of_o violence_n the_o randons_n also_o and_o different_a mount_n of_o piece_n cause_v a_o great_a alteration_n not_o only_o of_o the_o far_o shoot_v of_o all_o piece_n but_o also_o of_o their_o violent_a battery_n and_o albeit_o the_o different_a alteration_n be_v very_o intricate_a and_o strange_a yet_o have_v they_o a_o theericke_a certain_a theor._n 27._o there_o be_v also_o many_o other_o accidental_a alteration_n happen_v by_o reason_n of_o the_o wind_n the_o thickness_n or_o thinness_n of_o the_o air_n the_o heat_n or_o cool_v of_o the_o piece_n the_o different_a manner_n of_o charge_v by_o ram_v fast_o or_o loose_v the_o powder_n by_o close_a or_o loose_a roll_a or_o lie_v of_o the_o bullet_n by_o the_o unequal_a recule_n of_o the_o piece_n in_o his_o carriage_n or_o deformity_n of_o the_o axtree_n with_o diverse_a other_o such_o like_a whereof_o no_o rule_n certain_a can_v be_v prescribe_v to_o reduce_v these_o uncertain_a difference_n to_o any_o certain_a proportion_n but_o all_o these_o be_v by_o practice_n discretion_n and_o judgement_n to_o be_v consider_v and_o uniform_o guide_v and_o perform_v in_o their_o best_a perfection_n theor._n 28._o any_o piece_n mount_v 90._o grade_n above_o the_o horizon_n throw_v his_o bullet_n most_o violent_o immediate_o after_o the_o discharge_n and_o then_o the_o motion_n grow_v flower_n till_o the_o bullet_n be_v come_v to_o his_o utmost_a altitude_n and_o then_o by_o perpendicular_a fall_n increase_v by_o little_a and_o little_a his_o swiftness_n again_o even_o till_o it_o come_v to_o the_o horizon_n but_o at_o all_o other_o randons_n it_o fall_v not_o so_o out_o theor._n 29._o albeit_o in_o the_o subtlety_n of_o geometrical_a demonstration_n no_o part_n of_o the_o bullet_n violent_a motion_n can_v be_v true_o aver_v a_o right_n or_o direct_a line_n save_v only_o the_o perpendicular_a yet_o in_o these_o experiment_n mechanical_a that_o first_o part_n of_o the_o violent_a motion_n i_o mean_v so_o far_o as_o the_o piece_n be_v say_v to_o carry_v pointblank_a be_v so_o near_o the_o direct_a be_v and_o may_v well_o be_v term_v the_o direct_a line_n as_o all_o water_n level_v be_v account_v in_o all_o mechanical_a operation_n the_o perfect_a level_v and_o direct_v line_n albeit_o the_o subtlety_n of_o geometrical_a demonstration_n do_v find_v they_o not_o right_a or_o direct_v but_o curue_a or_o circular_a theor._n 30._o when_o any_o piece_n be_v mount_v direct_o to_o the_o zenith_n then_o do_v his_o motion_n violent_a be_v in_o that_o situation_n direct_o opposite_a to_o the_o natural_a carry_v the_o bullet_n in_o a_o perfect_a right_a line_n direct_o upward_a till_o the_o force_n of_o the_o violence_n be_v spend_v and_o the_o natural_a motion_n have_v get_v the_o victory_n and_o then_o do_v the_o natural_a return_n the_o bullet_n downward_o again_o by_o the_o very_a same_o perpendicular_a line_n and_o so_o be_v the_o whole_a motion_n of_o the_o bullet_n in_o this_o case_n a_o very_o direct_v perpendicular_a to_o the_o horizon_n theor._n 31._o but_o if_o any_o piece_n be_v discharge_v upon_o any_o angle_n of_o randon_n albeit_o the_o violent_a motion_n contend_v to_o carry_v the_o bullet_n direct_o by_o the_o line_n diagonall_a yet_o the_o perpendicular_a motion_n be_v not_o direct_o opposite_a do_v though_o unsensible_o even_o from_o the_o begin_n by_o little_a and_o little_a draw_v it_o from_o that_o direct_a and_o diagonall_a course_n and_o as_o the_o violent_a do_v decay_v so_o do_v the_o natural_a increase_n and_o of_o these_o two_o right_n line_v motion_n be_v make_v that_o mix_v curue_a helicall_a circuit_n of_o the_o bullet_n theor._n 32._o any_o piece_n therefore_o discharge_v at_o any_o mount_n or_o randon_n first_o throw_v forth_o her_o bullet_n direct_o a_o certain_a distance_n call_v of_o some_o gunner_n their_o pointblank_a range_v and_o then_o it_o make_v a_o curue_a decline_a ark_n and_o after_o finish_v either_o in_o a_o direct_a line_n or_o nigh_o incline_v towards_o it_o theor._n 33._o the_o further_a that_o any_o piece_n shoot_v in_o her_o direct_a line_n common_o call_v pointblank_a the_o deep_a also_o she_o pierce_v in_o her_o battery_n if_o the_o bullet_n be_v not_o of_o substance_n brickle_z or_o frangeable_a theor._n 34._o the_o more_o ponderous_a a_o bullet_n be_v the_o more_o it_o shake_v in_o battery_n albeit_o it_o pierce_v not_o always_o so_o deep_a as_o the_o light_a or_o lesser_a shot_n convenient_o charge_v theor._n 35._o any_o two_o piece_n of_o battery_n ordinance_n charge_v with_o one_o kind_n of_o bullet_n and_o shoot_v into_o one_o rampire_n of_o massy_a uniform_a kind_n of_o substance_n shall_v ever_o make_v their_o profundity_n of_o pierce_a proportional_a to_o their_o level_n range_v horizontall_a and_o if_o they_o be_v discharge_v either_o level_a or_o at_o one_o grave_n of_o random_n and_o at_o like_a distance_n theor._n 36._o any_o two_o piece_n of_o battery_n discharge_v into_o any_o rampart_n of_o uniform_a massy_a substance_n shall_v ever_o make_v their_o pierce_a depth_n proportional_a to_o their_o line_n diagonall_a albeit_o these_o piece_n be_v discharge_v from_o different_a randons_n so_o as_o they_o batter_v at_o like_a distance_n theor._n 37._o as_o archimedes_n line_n helicall_a or_o spirall_n be_v make_v by_o the_o direct_a motion_n of_o a_o point_n carry_v in_o a_o right_a line_n while_o that_o right_a line_n be_v circular_o turn_v as_o semidiameter_n upon_o his_o circle_n centre_n so_o be_v this_o artillery_n helicall_a line_n of_o the_o bullet_n circuit_n create_v only_o by_o two_o right_a line_v motion_n become_v more_o or_o less_o curue_a according_a to_o the_o difference_n of_o their_o angle_n occasion_v by_o the_o several_a angle_n of_o the_o random_n whereupon_o by_o demonstration_n geometrical_a a_o theoric_n may_v be_v frame_v that_o shall_v deliver_v a_o true_a and_o perfect_a description_n of_o those_o helicall_a line_n at_o all_o angles_n make_v between_o the_o horizon_n and_o the_o peeces-line_n diagonall_a theor._n 38._o these_o direct_a or_o diagonall_a line_n be_v always_o long_a when_o the_o piece_n axis_n be_v direct_v to_o the_o zenith_n and_o always_o as_o the_o piece_n axis_n decline_v more_o and_o more_o to_o the_o horizon_n so_o do_v the_o diagonall_a line_n grow_v short_a and_o at_o the_o level_a horizontall_a short_a of_o all_o theor._n 39_o these_o direct_a line_n diagonall_a albeit_o they_o increase_v in_o length_n at_o every_o grave_n of_o random_n from_o the_o horizon_n to_o the_o zenith_n yet_o be_v not_o their_o increase_n uniform_a or_o proportional_a either_o to_o their_o degree_n of_o randon_n or_o horizontall_a range_v nor_o yet_o to_o their_o circuit_n or_o altitude_n and_o yet_o such_o as_o may_v be_v reduce_v to_o a_o theoric_n certain_a theor._n 40._o the_o middle_a curue_a ark_n of_o the_o bullet_n circuit_n compound_v of_o the_o violent_a and_o natural_a motion_n of_o the_o bullet_n albeit_o they_o be_v indeed_o mere_a helicall_a yet_o have_v they_o a_o very_a great_a resemblance_n of_o the_o arke_n conicall_a and_o in_o randons_n above_o 45._o they_o do_v much_o resemble_v the_o hyperbole_n and_o in_o all_o under_o the_o ellipsis_n but_o exact_o they_o never_o accord_v be_v indeed_o spirall_n mix_v and_o helicall_a theor._n 41._o any_o piece_n discharge_v at_o any_o one_o random_n with_o like_a bullet_n and_o several_a charge_n of_o powder_n shall_v make_v both_o their_o line_n diagonall_a and_o curue_a circuit_n of_o different_a longitude_n but_o the_o curue_a arke_n shall_v always_o be_v as_o parallel_n and_o their_o longitude_n proportional_a to_o their_o line_n diagonall_a theor._n 42._o the_o last_o decline_a line_n of_o the_o bullet_n circuit_n albeit_o it_o seem_v to_o approach_v some_o what_o to_o the_o nature_n of_o a_o direct_a line_n again_o yet_o be_v it_o indeed_o still_o helicall_a and_o mix_v so_o long_o as_o there_o remain_v any_o part_n of_o the_o motion_n violent_a but_o after_o that_o be_v clean_o spend_v the_o rest_n of_o his_o course_n to_o the_o horizon_n be_v direct_v and_o perpendicular_a and_o a_o perfect_a right_a line_n indeed_o which_o be_v best_a discern_v in_o those_o grade_n of_o randon_n which_o be_v between_o the_o zenith_n and_o the_o mount_n or_o randon_n aequorizontall_a theor._n 43._o this_o decline_a line_n do_v always_o make_v a_o great_a and_o great_a angle_n with_o the_o horizon_n as_o you_o raise_v the_o piece_n to_o a_o great_a mount_n till_o you_o come_v to_o the_o mount_n aequorizantall_n about_o which_o point_n the_o same_o decline_a line_n become_v perpendicular_a before_o the_o bullet_n fall_v to_o the_o horizon_n theor._n 44._o the_o horizontall_a range_v in_o all_o piece_n mount_v from_o the_o horizon_n towards_o the_o zenith_n do_v not_o still_o increase_v but_o at_o every_o grade_n of_o randon_n be_v long_o till_o you_o come_v to_o the_o point_n